416 research outputs found
Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns
In this paper we consider a like-queue production system in which server startup
and breakdowns are possible. The server is turned on (i.e. begins startup)
when N units are accumulated in the system and off when the system is empty.
We model this system by an M[x]/M/1 queue with
server breakdowns and startup time under the N policy. The arrival rate varies according to the server's status:
off, startup, busy, or breakdown.
While the server is working, he is subject to
breakdowns according to a Poisson process. When the server breaks down, he requires repair
at a repair facility, where the repair time follows the negative exponential distribution.
We study the steady-state behaviour of the system size distribution at
stationary point of time as well as the queue size distribution at departure point of time
and obtain some useful results.
The total expected cost function per unit time is developed to determine the optimal operating
policy at a minimum cost. This paper provides the minimum expected cost and the optimal operating
policy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided
Performance improvement of remanufacturing systems operating under N-policy
This thesis deals with N-policy M/G/1 queueing remanufacturing system with general server breakdown and start-up time, where the value of returned products exponentially deteriorates since received. The server will instantly turn on the system, but the system requires a start-up period to prepare for remanufacturing when returned products in the queue reach the value of N. Otherwise, the system keeps in turn-off status. During the remanufacturing process, the machines may break down and will return back to service immediately after repairing. The procedures that will be used to achieve the target are as follows. Firstly, the expression of cost function will be derived and solved. Next, the simulation software ProModel will be used to simulate this problem. Finally, a sensitivity analysis is used on a numerical example to show the applicability of the methodology and quality of results
On M/G/1 system under NT policies with breakdowns, startup and closedown
AbstractThis paper studies the vacation policies of an M/G/1 queueing system with server breakdowns, startup and closedown times, in which the length of the vacation period is controlled either by the number of arrivals during the vacation period, or by a timer. After all the customers are served in the queue exhaustively, the server is shutdown (deactivates) by a closedown time. At the end of the shutdown time, the server immediately takes a vacation and operates two different policies: (i) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or the waiting time of the leading customer reaches T units; and (ii) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or T time units have elapsed since the end of the closedown time. If the timer expires or the number of arrivals exceeds the threshold N, then the server reactivates and requires a startup time before providing the service until the system is empty. If some customers arrive during this closedown time, the service is immediately started without leaving for a vacation and without a startup time. We analyze the system characteristics for each scheme
The Mx/G/1 Queue with Unreliable Server, Delayed Repairs, and Bernoulli Vacation Schedule under T-Policy
In this paper we study a batch arrival queuing system. The server may break down while delivering service. However, repair is not provided immediately, rather it is delayed for a random amount of time. At the end of service, the server may process the next customer if any are available, or may take a vacation to execute some other job. Finally, the server implements the T-policy. We describe for this system an optimal management policy. Numerical examples are provided
On transient queue-size distribution in the batch arrival system with the N-policy and setup times
In the paper the queueing system with the -policy and setup times is considered. An explicit formula for the Laplace
transform of the transient queue-size distribution is derived using
the approach consisting of few steps. Firstly, a "special\u27\u27
modification of the original system is investigated and, using the
formula of total probability, the analysis is reduced to the case
of the corresponding system without limitation in the service. Next,
a renewal process generated by successive busy cycles is used to
obtain the general result. Sample numerical computations
illustrating theoretical results are attached as well
On transient queue-size distribution in the batch arrival system with the N-policy and setup times
In the paper the queueing system with the -policy and setup times is considered. An explicit formula for the Laplace
transform of the transient queue-size distribution is derived using
the approach consisting of few steps. Firstly, a "special\u27\u27
modification of the original system is investigated and, using the
formula of total probability, the analysis is reduced to the case
of the corresponding system without limitation in the service. Next,
a renewal process generated by successive busy cycles is used to
obtain the general result. Sample numerical computations
illustrating theoretical results are attached as well
Control of a tandem queue with a startup cost for the second server
Various systems across a broad range of applications contain tandem queues. Strong dependence between the servers has proven to make such networks complicated and difficult to study. Exact analysis is rarely computationally tractable and sometimes not even possible. Nevertheless, as it is most often the case in reality, there are costs associated with running such systems, and therefore, optimizing the control of tandem queues is of main interest from both a theoretical and a practical point of view. Motivated by this, the present paper considers a tandem queueing network with linear holding costs and a startup cost for the second server. In our work, we present a rather intuitive, easy to understand, and at the same time very accurate technique to approximate the optimal decision policy. Extensive numerical experimentation shows that the approximation works extremely well for a wide range of parameter combinations
A dynamic ridesharing dispatch and idle vehicle repositioning strategy with integrated transit transfers
We propose a ridesharing strategy with integrated transit in which a private
on-demand mobility service operator may drop off a passenger directly
door-to-door, commit to dropping them at a transit station or picking up from a
transit station, or to both pickup and drop off at two different stations with
different vehicles. We study the effectiveness of online solution algorithms
for this proposed strategy. Queueing-theoretic vehicle dispatch and idle
vehicle relocation algorithms are customized for the problem. Several
experiments are conducted first with a synthetic instance to design and test
the effectiveness of this integrated solution method, the influence of
different model parameters, and measure the benefit of such cooperation.
Results suggest that rideshare vehicle travel time can drop by 40-60%
consistently while passenger journey times can be reduced by 50-60% when demand
is high. A case study of Long Island commuters to New York City (NYC) suggests
having the proposed operating strategy can substantially cut user journey times
and operating costs by up to 54% and 60% each for a range of 10-30 taxis
initiated per zone. This result shows that there are settings where such
service is highly warranted
Analysis of Batch Arrival Single and Bulk Service Queue with Multiple Vacation Closedown and Repair
In this paper, we analyze batch arrival single and bulk service queueing model with multiple vacation, closedown and repair. The single server provides single service if the queue size is ‘\u3c a’ and bulk service if the queue size is ‘ ≥ a’. After completing the service (single or bulk), the server may breakdown with probability ξ and then it will be sent for repair. When the system becomes empty or the server is ready to serve after the repair but no one is waiting, the server resumes closedown and then goes for a multiple vacation of random length. Using supplementary variable technique, the steady-state probability generating function (PGF) of the queue size at an arbitrary time is obtained. The performance measures and cost model are also derived. Numerical illustrations are presented to visualize the effect of system parameters
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